1. Field of the Invention
The present invention relates in general to an image transformation method and apparatus, and a storage medium, and more particularly to: a method of converting image data into high frequency components and low frequency components of a plurality of frequency bands and apparatus therefor; an image composition method of reconstructing the image data from the high frequency components and low frequency components and method therefor, an image data compression method of obtaining compressed data by compressing the high frequency components and low frequency components and apparatus therefor, an image decompression method of decompressing the compressed data and apparatus therefor, an image processing method of and apparatus for performing image processing employing an image transformation method and apparatus therefor and an image composition method of and apparatus therefor, as well as a computer readable storage medium for recording a program causing a computer to execute an image transformation method, an image composition method, an image compression method and an image decompression method.
2. Description of the Related Art
The practice of obtaining image data, subjecting the obtained image data to appropriate image processing, and then reproducing the image data is in wide use in various fields. One such proposed method of processing image data utilizes multiple-resolution transformation, and comprises converting an image into multiple-resolution images of a plurality of frequency bands, subjecting the image from each frequency band to a predetermined processing, and by performing reverse transformation on the processed images, obtaining a final processed image. The processing employed in this case, more specifically, comprises separating the high frequencies in order to remove noise, and performing compression processing by removing the data of frequency bands high in noise, etc.
In addition, wavelet transform, Laplacian Pyramid transform, and Fourier transform are known methods of performing multiple-resolution transformation. In particular, although wavelet transform is one method of analyzing//breaking down the frequencies of a signal, compared to the widely used Fourier transform, which is similar method of breaking down frequencies, because of the point that the ease with which locally changed data is detected is superior, wavelet transform has been in the limelight in recent years in just about every signal processing field (refer to: Oliver Rioul and Martin Vetterli, “Wavelets and Signal Processing”, IEEE SP Magazine, pp. 14-38, October 1991; Stephane Mallat, “Zero-Crossings of a Wavelet Transform, IEEE Transactions on Information Theory, Vol. 37, No. 4, pp. 1019-1033, July 1991; Japanese Unexamined Patent Publication Nos. 6(1994)-274614, 6(1994)-350989, 6(1994)-350990, 7(1995)-23228, 7(1995)-23229 and 7(1995)-79350.
According to the wavelet transforms disclosed in aforementioned Japanese Unexamined Patent Publication No. 6(1994)-274614, etc., by repeatedly performing a one-dimensional wavelet transform while sub-sampling vertically and horizontally is carried out, a multiple-resolution image such as that shown in FIG. 18 is obtained; this is called a tensor multiplied type two-dimensional wavelet transform. On the other hand, a method in which a wavelet transform is performed while sub-sampling is carried out in a checkered pattern (refer to The Red-Black Wavelet Transform, Greet Uytterhoeven, Adhemar Bultheel, Katholieke Universiteit Leuven, Report TW271, December 1997). This type of method, in which “liftin” is utilized, is called an unseparated-type wavelet transform, and for cases in which as shown in FIG. 19, pixels are disposed at vertical and horizontal, etc., intervals (hereinafter referred as square-patterned disposition), and a wavelet transform is repeatedly performed while the image is separated into an image formed of pixels disposed only at the positions indicated by an ‘O’ or ‘X’ mark. Hereinafter, this unseparated-type wavelet transform utilizing lifting will be explained. Note that when pixels are disposed only at positions indicated by the O and X marks as in FIG. 19, this is called checkered disposition.
FIG. 20 is provided for explanation of wavelet transform dependent on lifting. Note that for the sake of simplicity in explanation, a case in which a wavelet transform is performed on one-dimensional data is explained. First, one-dimensional data λj, i (here, the frequency band becomes a low frequency band corresponding to the high-low represented by j, and i is the element number) are separated into an odd-number component λj,2i formed of the pixels of the odd-number positions, and an even-number component λj,2i formed of the pixels of the even-number positions. Then, the even-number component λj,2i is subjected to low-pass filtering by low-pass filter LP1, and the resultant is subtracted from the odd-number component λj,2i; the component obtained by the subtraction operation is the high-frequency component γj+1. On the other hand, high-frequency component γj+1 is subjected to low-pass filtering by low-pass filter LP2, and the resultant is added to even-number component λj,2i; the component obtained from the addition operation is the low-frequency component λj+1. Then, by repeatedly subjecting the obtained low-frequency component λj1 to the same type of processing, data λj, I can be wavelet transformed.
On the other hand, reverse transformation of the data obtained by wavelet transform dependent on lifting is performed as described below. FIG. 21 is provided for explanation of reverse transformation of data obtained by a wavelet transform dependent on lifting. Note that, here, an explanation for a case in which is data λj, i is obtained from high-frequency component γj+1 and low-frequency component λj+1 will be given. Reverse transformation comprises performing processing completely the reverse of the wavelet transform shown in FIG. 20: high-frequency component γj+1 is subjected to low-pass filtering by low-pass filter LP2, and the resultant is subtracted from low-frequency component λj+1, whereby even-number component λj,2i is obtained; on the other hand, even-number component λj,2i is subjected to low-pass filtering by low pass filter LP1, and the resultant is added to high-frequency component γj+1, whereby odd-number component j,2i+1 is obtained; then even-number component λj,2i and odd-number component λj,2i+1 are combined to obtain data.
By repeatedly performing this type of lifting-dependent wavelet transform on a two-dimensional image, as that shown in FIG. 22, a multiple-resolution image is obtained. Note that in FIG. 22, the wavelet transform is repeated four times, and the low frequency component is shown as Li and the frequency component is shown as Hi (i=1-4). Note that by subjecting two-dimensional data to a lifting-dependent wavelet transform and carrying out the data sub-sampling in a checkered pattern, an unseparated-type wavelet transform can be realized, and by this unseparated-type wavelet transform, the high-frequency component Hi and the low-frequency component Li obtained in each step of the wavelet transform become arranged as elements (because it is not image data and cannot be called a pixel, it is hereinafter called an element) in a checkered pattern. In FIG. 22, because the high-frequency component Hi and the low-frequency component Li obtained in each step of the wavelet transform are shown arranged as elements in a square-pattern, high-frequency components H1, H3 and low-frequency components L1, L3 are shown rotated by 45°.
According to this unseparated-type wavelet transform utilizing lifting, the low-frequency component L4 obtaining in the final step and the high-frequency components Hi of all of the frequency bands are saved, and by performing reverse wavelet transformation on these, the original image can be completely reproduced.
On the other hand, the object of performing a wavelet transform is to separate the image into correlated low frequency components and to reduce the power of each component by performing multiple resolution transformation on the image. Because of this, it is preferable that the value of the elements of which the high-frequency components obtained in the wavelet transform are constructed is concentrated at 0. For example, for cases in which a wavelet transform is employed to compress an image, the compression ratio is improved as the number of elements whose value is 0 or close to 0 becomes greater, and for an image of the same compression ratio, the deterioration to the image quality is less.
Here, the comparative effect on the high-frequency component for tensor-multiplied type wavelet transforms and unseparated-type wavelet transforms utilizing lifting are shown in Chart 1 below. Note that, here, for both aforementioned types of wavelet transforms, when the low-frequency components have become {fraction (1/16)} the size of those of the original image, the ratio of the high-frequency components whose absolute value have become less than a predetermined value (1, 2, 3) has been obtained, and the comparison of this ratio is shown.
CHART 1=0≦1≦2Image 1Tensor-multiplied Type8.56%21.58%30.06%Unseparated-type9.10%22.25%30.35%Image 2Tensor-multiplied Type4.96%12.89%18.70%Unseparated-type4.96%12.08%16.99%
As shown in Chart 1, there are many elements in the image 1 subjected to an unseparated-type wavelet transform utilizing lifting whose value is 0 or close to zero, and a favorable result is thereby attained; however, the result obtained in the image 2, which has been subjected to a tensor-multiplied wave transform, the result is more favorable. This is because image 1 is a natural body and there is no anisotropy with respect to the horizontal and vertical directions, whereas image 2 is a building or man-made object, in which there is substantial anisotropy in the horizontal and vertical directions, and for images having anisotropy, such as image 2, it is easy for the value of the high-frequency component of the direction along the edge to become a value close to 0 with the performance of a tensor-multiplied wavelet transform, which has anisotropy in the same directions.
In this way, because there is no anisotropy in an unseparated-type wavelet transform utilizing lifting, when there is no image anisotropy, many high-frequency components having 0 or a value close to 0 can be obtained. However, for an image such as the image 2 described above having substantial anisotropy, because there are cases in which high-frequency components having a value of 0 or close to 0 can be obtained performing a tensor-multiplied wavelet transform, it is desirable that for images having substantial anisotropy as well, many high-frequency components having a value of 0 or close to 0 are obtained.